Topological Superfluid in a Fermi-Bose Mixture with a High Critical Temperature

We show that a 2D spin-polarized Fermi gas immersed in a 3D Bose-Einstein condensate constitutes a very promising system for realizing a $p_x+i{p}_y$ superfluid. The fermions attract each other via an induced interaction mediated by the bosons, and the resulting pairing is analyzed with retardation effects fully taken into account. This is further combined with Berezinskii-Kosterlitz-Thouless (BKT) theory to obtain reliable results for the superfluid critical temperature. We show that both the strength and the range of the induced interaction can be tuned experimentally, which can be used to make the critical temperature approach the maximum value allowed by general BKT theory. Moreover, this is achieved while keeping the Fermi-Bose interaction weak so that three-body losses are small. Our results show that realizing a topological superfluid with atomic Fermi-Bose mixtures is within experimental reach.

Figure 1

The zero-frequency $p$-wave interaction at the Fermi surface as a function of $n_F^{1/2}/n_B^{1/3}$ for a weakly interacting ${}^{40}\mathrm{K}\text{−}{}^7\mathrm{Li}$ mixture with $(n_B{a}_{\mathrm{eff}}^3{)}^{1/3}=0.1$. Here, ${\mathcal{N}}_F=m_F/2\pi$ is the density of states of the Fermi gas.

Figure 2

The superfluid critical temperatures as a function of $(n_B{a}_B^3{)}^{1/3}$ (on a logarithmic scale) for the mixture with $n_F^{1/2}/n_B^{1/3}=0.1$ and $(n_B{a}_{\mathrm{eff}}^3{)}^{1/3}=0.1$. (Inset) The behavior of $v_F/c_0$ as a function of $(n_B{a}_B^3{)}^{1/3}$.

Figure 3

The BKT temperatures as a function of $(n_B{a}_B^3{)}^{1/3}$ (on a logarithmic scale) for the ${}^{40}\mathrm{K}\text{−}{}^7\mathrm{Li}$ mixture for various parameter settings, namely, for ($a$) $n_F^{1/2}/n_B^{1/3}=0.1$ and $(n_B{a}_{\mathrm{eff}}^3{)}^{1/3}=0.1$ (the black solid line), ($b$) $n_F^{1/2}/n_B^{1/3}=0.5$ and $(n_B{a}_{\mathrm{eff}}^3{)}^{1/3}=0.15$ (the red dashed line), and ($c$) $n_F^{1/2}/n_B^{1/3}=0.8$ and $(n_B{a}_{\mathrm{eff}}^3{)}^{1/3}=0.2$ (the blue dash-dotted line).